Telecommunication systems are widely deployed to provide various telecommunication services. A communications system may be characterized as a collection of transmitters, receivers, and communications channels that send messages to one another. The transmission of a raw electrical signal, i.e., baseband signal, has several limitations, including bandwidth limitations, distance limitations, etc. To address these issues, many different modulation techniques have been developed. Modulation involves encoding a baseband source signal Sm(t) onto a carrier signal. The carrier waveform is then varied in a manner directly related to the baseband signal.
The move to digital modulation provides more information capacity, compatibility with digital data services, higher data security, better quality communications, and quicker system availability. Digital modulation converts information-bearing discrete-time symbols into a continuous-time waveform. The choice of digital modulation scheme will significantly affect the characteristics, performance and resulting physical realization of a communication system. Traditional linear modulation systems map collections of data bits to a point in a two-dimensional space, 2, e.g., binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), 16-state quadrature amplitude modulation (16-QAM). For example, relatively simple modulation such as QPSK offers excellent bit error rate (BER) performance at relatively low signal strengths. QPSK however uses a large bandwidth. 16-QAM is more bandwidth efficient, but requires on stronger signal strength than QAM to achieve a low BER. This is particularly so for the more dense bandwidth schemes such as 64-state QAM (64-QAM).
There are three characteristics of a signal that are typically changed over time: amplitude, phase, or frequency. Note that phase and frequency are related. Amplitude and phase can be modulated simultaneously and independently. Such signals can also be represented by in-phase (I) and Quadrature (Q) components, which are the rectangular representation of the polar signals. It is common for digital modulations to map the data to a number of discrete points on the I/Q (complex) plane. These are known as constellation points.
Between symbol clock transitions, the carrier is modulated by an amplitude and phase or, equivalently, an I and Q value that maps to a constellation point in the complex plane. A constellation point encodes a specific data sequence, which includes one or more data bits. A constellation diagram shows the valid locations (i.e., the magnitude and phase relative to the carrier) for permitted symbols. To demodulate the incoming data, the exact magnitude and phase of the received signal is estimated. The layout of the constellation diagram and its ideal symbol locations is determined generically by the chosen modulation format.
Modulation symbols are used to represent information, wherein a symbol may represent one bit or a number of bits. In a symbol period, a digital modulator maps bits to a transmitted waveform from a pre-defined set of possible waveforms, wherein a waveform corresponds to an information symbol. However, existing modulation systems operate in the complex plane or R2. These systems do not rely on the topological of alternative spaces or path relative to such a space to directly carry information.